Opportunities and challenges in quantum-enhanced …...Opportunities and challenges for...
Transcript of Opportunities and challenges in quantum-enhanced …...Opportunities and challenges for...
AlejandroPerdomo-OrtizSeniorResearchScientist,QuantumAILab.atNASAAmes ResearchCenterandatthe
UniversitySpaceResearchAssociation,USAHonorarySeniorResearchAssociate,ComputerScienceDept.,UCL,UK
NationalHarbor,MD,September28,2017
Opportunitiesandchallengesinquantum-enhancedmachinelearninginnear-termquantumcomputers
QUBITSD-waveUserGroup2017
Funding:
Perdomo-Ortiz,Benedetti,Realpe-Gomez,andBiswas.arXiv:1708.09757 (2017).ToappearintheQuantumScienceandTechnology(QST)invitedspecialissueon“Whatwouldyoudowitha1000qubit device?”
D-WaveSystemCapability1) As a discrete optimization solver:
2) As a physical device to sample from Boltzmann distribution:
Potential NASA applications: - planning- scheduling - fault diagnosis - graph analysis - communication networks, etc.
QUBO: Quadratic Unconstrained Binary Optimization (Ising model in physics jargon).
Computationally bottleneck
Our work: Benedetti et al. PRA 94, 022308 (2016)
• Algorithm uses the same samples that will be used for the estimation of the gradient
• We provide a robust algorithm to estimate the effective temperature of problem instances in quantum annealers.
NP-hard problem
⇠(s1, ..., sN ) =NX
j=1
hjsj +NX
i,j2E
Jijsisj
Given {hj, Jij}, find {sk = ± 1}that minimizes
P
Boltzman
/ exp[�⇠(s1, ..., sN )/Teff
]
Early work:Bian et al. 2010. The Ising model: teaching an old problem new tricks.
Follow-up work:Raymond et al. Global warming: Temperature estimation in annealers. Frontiers in ICT, 3, 23 (2016).
Widely used in unsupervised learning
Visible units
Hidden unitsRBM
Potential NASA applications: - machine leaning (e.g., training
of deep-learning networks)
Learning algorithm
MODELP ( Image )
DATASET
Unsupervised learning (generative models)
NO LABELS
Learn the “best” model distribution that can generate the same kind of data
Learning algorithm
MODELP ( Image )
LEARNED MODELP ( Image )
DATASET
Example application:Image reconstruction
Damaged image
Unsupervised learning (generative models)
NO LABELS
Learn the “best” model distribution that can generate the same kind of data
Reconstructed image
Learning algorithm
MODELP ( Label | Image )
LEARNED MODELP ( Label | Image )
Supervised learning (discriminative models)
Learn the “best” model that can perform a specific task
Example application:Image recognition
Predicted label
Image to be recognized
61
26624 98 66 175
Labels
DATASET
Anear-termapproachforquantum-enhancedmachinelearningState-of-the-artQML
- NeedforqRAM (caseofmostgate-basedproposal).
- Qubitsrepresentvisibleunits;issueforcaseoflargedatasets
- Mostpreviousproposedworkhavehighlyoptimizedpowerfulclassicalcounterparts(e.g.,ondiscriminative/classificationtasks)
Probabilistic programming
Potential impact across social and natural sciences, engineering, and more
Hypothesis: intractable sampling problems enhanced by quantum sampling
Deeplearning Others...Bayesian
inference
Lesson1:MovetointractableproblemsofinteresttoMLexperts(e.g.,generativemodelsinunsupervisedlearning).
Anear-termapproachforquantum-enhancedmachinelearning
Lesson2:Needfornovelhybridapproaches.
LEARNING
Stochastic gradient descent
Θt+1 = Θt + G [ P(s|Θt) ]
PREDICTIONS
F [ P(s|Θt) ]
HARD TO COMPUTE
Estimation assisted by sampling from quantum computer
DATA
s = {s1,…, sD}
Computationally bottleneck
Widely used in unsupervised learning
Visible units, v
Hidden units, uRBM
Ex.:RestrictedBoltzmannMachines(RBM)
hviujip(v,u)Where,p(v,u) =
e�E(v,u|✓)/Teff
Z(✓)
Perdomo-Ortiz,etal.OpportunitiesandChallenges inQuantum-AssistedMachineLearninginNear-termQuantumComputer.arXiv:1708.09757.(2017).
Benedetti,etal.Quantum-assistedlearningofgraphicalmodelswitharbitrarypairwiseconnectivity.arXiv:1609.02542 (2016).
Benedetti,etal.Estimationofeffectivetemperaturesinquantumannealers forsamplingapplications:Acasestudywithpossibleapplicationsindeeplearning.PRA 94,022308(2016).
Benedetti,etal.Quantum-assistedHelmholtzmachines:Aquantum-classicaldeeplearningframeworkfor industrialdatasetsinnear-termdevices.arXiv:1708.09784 (2017).
Challengessolved:
X
v2D
@ lnL(✓|v)@Jij
/ hviujidata � hviujimodel
Anear-termapproachforquantum-enhancedmachinelearning
Challengesofthehybridapproach:
- Needtosolveclassical-quantummodelmismatch
Training Method: Stochastic gradient ascent
Benedettietal.Phys.Rev.A94,022308(2016)
Classical Quantum-Teff?
Nosignificantprogressin2010-2015forgenerativemodelingandQAsampling.
Visibleunits Hiddenunits
Anear-termapproachforquantum-enhancedmachinelearning
Resolvingmodelmismatchallowsforrestartingfromclassicalpreprocessing
Benedettietal.Phys.Rev.A94,022308(2016)
0 200 400 600 800 1000�11
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�8
�7
�6
L av
(a)
With Bias CorrectionWithout Bias Correction
0 200 400 600 800 1000�11
�10
�9
�8
�7
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L av
(b)
With Importance SamplingWithout Importance Sampling
0 100 200 300 400 500iteration
�11
�10
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L av
(c)QuALe @ TDW2X = 0.033 with RestartQuALe @ Te↵ with RestartCD-1
Anear-termapproachforquantum-enhancedmachinelearning
Challengesofthehybridapproach:
Benedettietal.arXiv:1609.02542
Fullyvisiblemodels
Visibleunits
- Robustnesstonoise,intrinsiccontrolerrors,andtodeviationsfromsamplingmodel(e.g.,Boltzmann)
- Curseoflimitedconnectivity – parametersetting
- Needtosolveclassical-quantummodelmismatch
Training Method: Stochastic gradient ascent
Benedettietal.Phys.Rev.A94,022308(2016)
Classical Quantum-Teff?
X
v2D
@ lnL(✓|v)@Jij
/ hviujidata � hviujimodel
Visibleunits Hiddenunits
Nosignificantprogressin2010-2015forgenerativemodelingandQAsampling.
Quantum-assistedunsupervisedlearningondigits
OptDigits Datasets
Dataset:OpticalRecognitionofHandwrittenDigits(OptDigits)
8x8 7x6 7x6,binarized
32x32
Quantum-assistedunsupervisedlearningondigits
OptDigits Datasets
Dataset:OpticalRecognitionofHandwrittenDigits(OptDigits)
Quantum-assistedunsupervisedlearningondigits
46fully-connectedlogical(visible)variables
940physicalqubits
- Aretheresultsfromthistrainingon940qubitexperimentmeaningful?
- Isthemodelcapableofgeneratingdigits?
42forpixels+4toone-hotencodetheclass(onlydigits1-4)
Overcomingthecurseoflimitedconnectivity inhardware.
Min.CL=12,Max.CL=28
Quantum-assistedunsupervisedlearningondigits
(quantum) machine
Human
Humanor(quantum)machine?(Turingtest)
Dataset:OpticalRecognitionofHandwrittenDigits(OptDigits)
Resultsfromexperimentsusing940qubits,withoutpost-processing.Thehardware-embeddedmodelrepresentsa46nodefullyconnectedgraph.
Anear-termapproachforquantum-enhancedmachinelearningChallengesofthehybridapproach:
Benedettietal.arXiv:1609.02542
Fullyvisiblemodels
Visibleunits
- Robustnesstonoise,intrinsiccontrolerrors,andtodeviationsfromsamplingmodel(e.g.,Boltzmann)
- Curseoflimitedconnectivity – parametersetting
Howaboutlargecomplexdatasetswithcontinuousvariables?Allpreviousfailtodothat(fullyquantumandhybridhere)
- Needtosolveclassical-quantummodelmismatch
Training Method: Stochastic gradient ascent
Benedettietal.Phys.Rev.A94,022308(2016)
Classical Quantum-Teff?
NoprogressinfiveyearssinceQAsamplingwasproposedasapromissingappplication.
Visibleunits Hiddenunits
Perspectiveonquantum-enhancedmachinelearning
Compresseddata
Rawinputdata
Measurement
Hiddenlayers
Inference
Qua
ntum
processing
Classicalpre-a
ndpost-p
rocessing
Visibleunits Hiddenunits Qubits
Trainingsamples
• Newhybridproposalthatworksdirectlyonalow-dimensionalrepresentationofthedata.
Perspectiveonquantum-enhancedmachinelearning
Compresseddata
i~d⇢✓(t)dt
= [H✓, ⇢✓]i~d⇢✓(t)
dt= [H✓, ⇢✓]
✓
Rawinputdata
Quantumsampling
Measurement
Hiddenlayers
ClassicalgenerationorreconstructionofdataIn
ference
Qua
ntum
processing
Classicalpre-a
ndpost-p
rocessing
Visibleunits Hiddenunits Qubits
Trainingsamples
Generatedsamples
• Newhybridproposalthatworksdirectlyonalow-dimensionalrepresentationofthedata.
Perspectiveonquantum-enhancedmachinelearning
Compresseddata
i~d⇢✓(t)dt
= [H✓, ⇢✓]i~d⇢✓(t)
dt= [H✓, ⇢✓]
✓
Rawinputdata
Quantumsampling
Measurement
Hiddenlayers
ClassicalgenerationorreconstructionofdataIn
ference
Qua
ntum
processing
Classicalpre-a
ndpost-p
rocessing
Visibleunits Hiddenunits Qubits
Corruptedimage
Reconstructedimage
• Newhybridproposalthatworksdirectlyonalow-dimensionalrepresentationofthedata.
Benedetti,Realpe-Gomez,andPerdomo-Ortiz.Quantum-assistedHelmholtzmachines:Aquantum-classicaldeeplearningframeworkforindustrialdatasetsinnear-termdevices.arXiv:1708.09784 (2017).
ExperimentalimplementationoftheQAHM
Experimentsusing1644qubits (nofurtherpostprocessing!)
Benedetti,Realpe-Gomez,andPerdomo-Ortiz.Quantum-assistedHelmholtzmachines:Aquantum-classicaldeeplearningframeworkforindustrialdatasetsinnear-termdevices.arXiv:1708.09784 (2017).
Max. CL = 43
Opportunities and challenges for quantum-assisted machine learning in near-termquantum computers
Alejandro Perdomo-Ortiz,1, 2, 3, ⇤ Marcello Benedetti,1, 3 John Realpe-Gomez,1, 4, 5 and Rupak Biswas6
1Quantum Artificial Intelligence Lab., NASA Ames Research Center, Mo↵ett Field, CA 94035, USA2USRA Research Institute for Advanced Computer Science (RIACS), 615 National, Mountain View CA 94043, USA
3Department of Computer Science, University College London, WC1E 6BT London, United Kingdom4SGT Inc., 7701 Greenbelt Rd., Suite 400, Greenbelt, MD 20770, USA
5Instituto de Matematicas Aplicadas, Universidad de Cartagena, Bolıvar 130001, Colombia6Exploration Technology Directorate, NASA Ames Research Center, Mo↵ett Field, CA 94035, USA
[Abstract here]
I. INTRODUCTION
With the advent of quantum computing technologiesnearing the era of commercialization and of quantumsupremacy [? ], it is a pressing task to think of potentialapplications that might benefit from these devices. Ma-chine learning stands out as a powerful statistical frame-work that have allowed for the solution of problems wheredeterministic algorithms are hard to develop. Examplesof such algorithms include image and voice recognition,medical applications [Marc: mention here other selectedkick ass app for ML]. The development of quantum algo-rithms that can assist or replace in it entirety the classi-cal ML routine is an ongoing e↵ort that has attracted alot of interest in the scientific quantum information com-munity. [cite all or most representative work here, e.g.,Dorband et al :’D]
Although the focus has been on tasks such as classifi-cation [cite Rebentrost, etc, etc], linear regression [cite],Gaussian models [cite Fitzsimmons] [find other represen-tative examples] corresponding to the most widely usednowadays by machine learning practitioners, we do notforesee these ones would be important for near-term usesof quantum computers. The same reasons that makethese techniques so popular, e.g., their scalability andalgorithmic e�ciency in tackling huge datasets, makesthese techniques less appealing to become top candi-dates as killer application in quantum machine learningwith devices in the range of 100-1000 qubits. In otherwords, to reach interesting industrial scale applicationsit would be required at least millions or even billionsof qubits before one make them competitive with classi-cal e�cient algorithms. This is even under the assump-tion of a quadratic or exponential speedup, which be-comes a mute advantage when dealing with real-worlddatasets and with the quantum devices to come in thenext decades nearing the 1000s of qubits regime. Only agame changer, as elaborated later on this perspective, forexample by introducing hybrid algorithms might be ableto also make a dent in speeding up such routine tasks.
In our perspective here, we propose and emphasize two
⇤Correspondence: [email protected]
approaches to maximize the possibilities of finding killerapplications on near-term quantum computers:
(i) Focus on problems that are currently hard and in-tractable for the ML community: For example,fully generative models, unsupervised and semi-supervised learning as described in Sec. II.
(ii) Focus on hybrid quantum algorithms that can beeasily integrated in the intractable step of the MLalgorithmic pipeline, as described in Sec. IV.
Each one of these tasks have their own challenges andsignificant work need to be done towards having experi-mental implementations on available quantum hardware(see e.g., [Benedetti1, Benedetti2]. Based on our pastexperience in implementing quantum-assisted ML algo-rithms on existing quantum hardware devices, we providehere some insights into the main challenges ahead in de-veloping such opportunities for QML. Although the focushere is on implementations on quantum annealers, we at-tempt to provide parallel insights in other computationalparadigms such as the gate model of quantum computa-tion. The guidance on which problems to be tackled isguided by our expertise in ML and by the advice fromexperts in the ML community.In Sec. II we present examples of domains in ML we
believe o↵er vlable opportunities for near-term quantumcomputers. In Sec. III we present the challenges ahead ofsuch implementations in real hardware, while in Sec. IVwe provide some advice on potential solutions to over-coming these challenges towards such implementations.In Sec. ?? we summarize our work.
II. OPPORTUNITIES IN QML
a. Scenarios where labeled data is scarce: Our fo-cus is on unsupervised learning techniques that canextract salient spatiotemporal features from unlabeleddata. This is important because one of the central as-pects of science is the discovery of unknown patterns;nobody tells scientists which patterns they should lookfor. This also serves as a pre-training phase that can sub-stantially reduce the amount of labeled data needed for
- Opportunities: EmphasisinmovingfrompopularMLtonot-so-popularbutstillhighlyvalueMLapplications.Example:Fromdiscriminativemodelstomorepowerfulgenerativemodels.Also,classicaldatasetswithintrinsicquantumcorrelations.
- Challenges: Limitedqubit-qubit connectivity,limitedprecision,intrinsiccontrolerrors,digitalrepresentation,classical-quantumfeedback(incaseofhybrid).
- Proposeddirections:Emphasisonhybridquantum-classicalalgorithms.Newapproachcapableoftacklinglargecomplexdatasetsinmachinelearning.
arXiv:1708.09757.(2017).ToappearintheQuantumScienceandTechnology(QST)invitedspecialissueon“Whatwouldyoudowitha1000qubitdevice?”
https://usra-openhire.silkroad.com/epostings/index.cfm?fuseaction=app.jobInfo&version=1&jobid=629
OpportunitiesatNASAQuantumAILab.(NASAQuAIL)atdifferentlevels:internships,postdoc,orResearchScientist.
Fordetails,pleasecontact:EleanorRieffel: NASAQuAIL Lead,or,AlejandroPerdomo-Ortiz:[email protected],[email protected]
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